Hausdorff maximal principle
In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset. The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over ZF (Zermelo–Fraenkel set theory without the axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33).
known for
Wikipage disambiguates
primaryTopic
Hausdorff maximal principle
In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset. The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over ZF (Zermelo–Fraenkel set theory without the axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33).
has abstract
Der Maximalkettensatz, auch al ...... swahlaxiom logisch äquivalent.
@de
El principio maximal de Hausdo ...... inita (como ) no es necesario.
@es
Il principio di massimalità di ...... mentre A per ipotesi non lo è.
@it
In de ordetheorie, een deelgeb ...... wski genoemd (Kelley 1955:33).
@nl
In mathematics, the Hausdorff ...... towski lemma (Kelley 1955:33).
@en
Twierdzenie Hausdorffa o łańcu ...... wnoważne z aksjomatem wyboru).
@pl
Принцип максимума Хаусдорфа (а ...... а эквивалентен аксиоме выбора.
@ru
Wikipage page ID
Wikipage revision ID
738,023,089
title
A proof of equivalence of Zorn ...... Hausdorff's maximum principle
Hausdorff's maximum principle
comment
Der Maximalkettensatz, auch al ...... swahlaxiom logisch äquivalent.
@de
El principio maximal de Hausdo ...... orial tiene al menos una base.
@es
Il principio di massimalità di ...... sarà ordinato parzialmente. Ma
@it
In de ordetheorie, een deelgeb ...... deelverzameling ligt besloten.
@nl
In mathematics, the Hausdorff ...... towski lemma (Kelley 1955:33).
@en
Twierdzenie Hausdorffa o łańcu ...... ciwy w żadnym innym łańcuchu).
@pl
Принцип максимума Хаусдорфа (а ...... а эквивалентен аксиоме выбора.
@ru
label
Hausdorff maximal principle
@en
Hausdorffs Maximalkettensatz
@de
Maximaal-principe van Hausdorff
@nl
Principio di massimalità di Hausdorff
@it
Principio maximal de Hausdorff
@es
Twierdzenie Hausdorffa o łańcuchu maksymalnym
@pl
Принцип максимума Хаусдорфа
@ru